Finite Group Databasebeta

← #11787529

Subgroups — #11787529

Order 1152.

1314 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D8C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#72037—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×C32×D8—22no—
13C2×C32×D8—22no—
14C2×C32×D8C414yescomplemented
15C22×C32×C8C2211yescharacteristic
16C2×#3757—21no—
17C2×#3757—21no—
18C2×#3757—21no—
19D4×C3⋊Dic3—22no—
20D4×C3⋊Dic3—22no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63659—22no—
26#63659—22no—
27C22×C3×D8D314yes—
28C2×D4×Dic3—34no—
29#5221—34no—
30C2×#832—34no—
31C2×#832—34no—
32#4551—34no—
33#4550—34no—
34C24×C32—21no—
35C24×C32—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4C2×C412yes—
45C2×C32×D4C2×C412yescomplemented
46C2×C32×D4D412yes—
47C2×C32×D4D412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—24no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—42no—
53C22×C3⋊Dic3—42no—
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C32×D8—28no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60#3757—24no—
61#3757—42no—
62#3757—42no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72#1879—91noSylow
73C22×C3×D4C2×D314yes—
74C22×C3×D4C2×D314yes—
75C23×Dic3—64no—
76C2×C3×D8—28no—
77C2×C3×D8—28no—
78C2×C3×D8Dic3116yescomplemented
79C22×C3×C8C2×D314yes—
80C2×#217—64no—
81C2×#217—64no—
82C2×#217—64no—
83D4×Dic3—68no—
84D4×Dic3—68no—
85C2×C4⋊Dic3—34no—
86C2×C4⋊Dic3—34no—
87C2×C4×Dic3—34no—
88C22×C3⋊C8—34no—
89#832—68no—
90#832—68no—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32—22no—
94C23×C32—22no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—41no—
101C23×C32—41no—
102C23×C32—41no—
103C23×C32—41no—
104C23×C32—41no—
105C23×C32C2×D411yescharacteristic
106C32×D4—22no—
107C32×D4—22no—
108C32×D4—22no—
109C32×D4—22no—
110C32×D4—22no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4C22⋊C414yescomplemented
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—48no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3D812yescomplemented
133C32×C8—22no—
134C3⋊(C3⋊C8)—41no—
135C22×D8C3⋊D311yescharacteristic
136C2×C4×D4—91no—
137C2×#102—91no—
138C2×#102—91no—
139#390—91no—
140#340—91no—
141#336—91no—
142C24×C3—24no—
143C24×C3—24no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4—24no—
150C2×C3×D4—24no—
151C2×C3×D4—24no—
152C2×C3×D4C2×Dic318yes—
153C2×C3×D4C2×Dic318yescomplemented
154C2×C3×D4#6718yes—
155C2×C3×D4#6718yes—
156C22×C3×C4C22×D314yes—
157C22×Dic3—34no—
158C22×Dic3—34no—
159C22×Dic3—616no—
160C22×Dic3—64no—
161C22×Dic3—64no—
162C22×Dic3—128no—
163C22×Dic3—128no—
164C3×D8—232no—
165C2×C3×C8—24no—
166C2×C3×C8—24no—
167C2×C3×C8C2×Dic318yescomplemented
168#217—616no—
169#217—128no—
170#217—128no—
171C4⋊Dic3—38no—
172C4⋊Dic3—64no—
173C4⋊Dic3—64no—
174C4⋊Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3—64no—
177C2×C3⋊C8—64no—
178C2×C3⋊C8—64no—
179C2×C3⋊C8—64no—
180C22×C32—24no—
181C22×C32—42no—
182C22×C32—42no—
183C22×C32—42no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32—42no—
190C22×C32—81no—
191C22×C32—81no—
192C22×C32—81no—
193C22×C32—81no—
194C22×C32C4×D411yescharacteristic
195C22×C32#12011yescharacteristic
196C22×C32#12111yescharacteristic
197C22×C32C2×D811yescharacteristic
198C22×C32#13511yescharacteristic
199C22×C32AGL(1,ℤ/8)11yescharacteristic
200C22×C32AGL(1,ℤ/8)11yescharacteristic
201C32×C4C2×C22⋊C411yescharacteristic
202C32×C4C4×D411yescharacteristic
203C32×C4#12111yescharacteristic
204C32×C4#12311yescharacteristic
205C3⋊Dic3—22no—
206C3⋊Dic3—42no—
207C3⋊Dic3—41no—
208C3⋊Dic3—81no—
209C22×D4C2×C3⋊D311yescharacteristic
210C22×D4C2×C3⋊D311yescharacteristic
211C23×C4—181no—
212C2×D8—22no—
213C2×D8—22no—
214C2×D8C3⋊Dic314yescomplemented
215C22×C8—91no—
216C22×C8C2×C3⋊D311yescharacteristic
217C4×D4—182no—
218C4×D4—182no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—91no—
221C2×C22⋊C4—181no—
222C2×C22⋊C4—181no—
223C2×C22⋊C4—181no—
224C2×C42—91no—
225#102—182no—
226#102—182no—
227C23×C3—28no—
228C23×C3—28no—
229C23×C3—28no—
230C23×C3—28no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3—44no—
234C23×C3—44no—
235C23×C3—44no—
236C23×C3—44no—
237C23×C3—44no—
238C23×C3—44no—
239C23×C3—44no—
240C23×C3—44no—
241C23×C3D3×D414yes—
242C3×D4—28no—
243C3×D4—28no—
244C3×D4—28no—
245C3×D4—28no—
246C3×D4—28no—
247C3×D4—44no—
248C3×D4—44no—
249C3×D4#217116yescomplemented
250C2×C3×C4D3×D414yes—
251C2×C3×C4#23714yes—
252C2×C3×C4#23714yes—
253C2×C3×C4C22×Dic314yes—
254C2×C3×C4C2×#6714yes—
255C2×C3×C4C2×#6714yes—
256C2×Dic3—38no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—68no—
263C2×Dic3—1232no—
264C2×Dic3—124no—
265C2×Dic3—124no—
266C2×Dic3—124no—
267C2×Dic3—124no—
268C2×Dic3—124no—
269C3×C8—28no—
270C3⋊C8—124no—
271C2×C32—44no—
272C2×C32—82no—
273C2×C32#38611yescharacteristic
274C2×C32C4×D811yescharacteristic
275C2×C32#44211yescharacteristic
276C2×C32#44711yescharacteristic
277C2×C32#44911yescharacteristic
278C2×C32#45911yescharacteristic
279C2×C32#46311yescharacteristic
280C24—21no—
281C24—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4C2×C3⋊Dic312yes—
291C2×D4C2×C3⋊Dic312yescomplemented
292C2×D4#63812yes—
293C2×D4#63812yes—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—184no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4—362no—
300C22×C4—362no—
301C22×C4C22×C3⋊D311yescharacteristic
302D8—28no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—181no—
306C2×C8—181no—
307C2×C8—181no—
308C2×C8C2×C3⋊Dic312yescomplemented
309C4⋊C4—92no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C22⋊C4—184no—
314C22⋊C4—362no—
315C22⋊C4—362no—
316C42—181no—
317C42—181no—
318C22×C3—216no—
319C22×C3—48no—
320C22×C3—48no—
321C22×C3—48no—
322C22×C3—48no—
323C22×C3—48no—
324C22×C3—48no—
325C22×C3—48no—
326C22×C3—48no—
327C22×C3—48no—
328C22×C3—84no—
329C22×C3—84no—
330C22×C3—84no—
331C22×C3—84no—
332C22×C3D3×D814yes—
333C22×C3#91114yes—
334C22×C3#91114yes—
335C22×C3#91214yes—
336C22×C3D4×Dic314yes—
337C22×C3#93714yes—
338C22×C3#93914yes—
339C3×C4D4×Dic314yes—
340C3×C4#93514yes—
341C3×C4#93914yes—
342C3×C4C2×#21714yes—
343Dic3—68no—
344Dic3—128no—
345Dic3—124no—
346Dic3—244no—
347C32#187911yescharacteristic, complemented, Sylow
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23D4×C3⋊D311yescharacteristic
363D4—22no—
364D4—22no—
365D4—22no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4#375714yescomplemented
371C2×C4—92no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—181no—
377C2×C4—182no—
378C2×C4—368no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4—361no—
382C2×C4—361no—
383C2×C4—361no—
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4#383011yescharacteristic
386C2×C4#383011yescharacteristic
387C2×C4C22×C3⋊Dic311yescharacteristic
388C2×C4C2×#63811yescharacteristic
389C2×C4C2×#63811yescharacteristic
390C8—22no—
391C8—361no—
392C2×C3—416no—
393C2×C3—88no—
394C2×C3Dic3×D814yes—
395C2×C3#515014yes—
396C2×C3#515214yes—
397C2×C3#515314yes—
398C2×C3#515614yes—
399C2×C3#515814yes—
400C2×C3#522014yes—
401C22—24no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22D8×C3⋊D311yescharacteristic
416C22#6412011yescharacteristic
417C22#6412011yescharacteristic
418C22#6412111yescharacteristic
419C22D4×C3⋊Dic311yescharacteristic
420C22#6414611yescharacteristic
421C22#6414811yescharacteristic
422C4—182no—
423C4—362no—
424C4—361no—
425C4—721no—
426C4D4×C3⋊Dic311yescharacteristic
427C4#6414411yescharacteristic
428C4#6414811yescharacteristic
429C4C2×#375711yescharacteristic
430C3#7203714yescomplemented
431C2—44no—
432C2—82no—
433C2D8×C3⋊Dic311yescharacteristic
434C2#1059284911yescharacteristic
435C2#1059285111yescharacteristic
436C2#1059285211yescharacteristic
437C2#1059285511yescharacteristic
438C2#1059285711yescharacteristic
439C2#1059291911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC22×C32×D8C2
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D8C3⋊D3
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. #10592920C2semidirect
4. C2×#63659C2semidirect
5. C2×#63659C2semidirect
6. #10589417C2semidirect
7. #10589416C2semidirect
14. C2×C32×D8C4semidirect
45. C2×C32×D4C2×C4semidirect
59. C2×C32×C8C2×C4semidirect
78. C2×C3×D8Dic3semidirect
113. C32×D4C22⋊C4semidirect
132. C2×C3⋊Dic3D8semidirect
153. C2×C3×D4C2×Dic3semidirect
167. C2×C3×C8C2×Dic3semidirect
214. C2×D8C3⋊Dic3semidirect
249. C3×D4#217semidirect
291. C2×D4C2×C3⋊Dic3semidirect
308. C2×C8C2×C3⋊Dic3semidirect
347. C32#1879semidirect
370. D4#3757semidirect
430. C3#72037semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C32×D82
C2×D4×C3⋊Dic32
#105929202
C2×#636592
#105894172
#105894162
#720373